The density of the $(\alpha ,\beta )$-superprocess and singular solutions to a fractional non-linear PDE

Thomas Hughes

We consider the density $X_t(x)$ of the critical $(\alpha ,\beta )$-superprocess in $R^d$ with $\alpha \in (0,2)$ and $\beta <\frac{\alpha }{d}$. A recent result from PDE implies a dichotomy for the density: for…